2010 BME 259 Problem Set 6 Solutions

C relate the shear stress at the vessel wall to the

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Unformatted text preview: ess at the vessel wall to the flow rate and show that the result from part (b), Murray's law, requires that the wall shear stress be constant. Solution Using equations for shear and flow rate from above, we can show that, Replacing Q with from above, As long as the metabolic consumption rate is constant, the shear stress is constant. 3. Problem 5.11 Most branching blood vessels consist of a parent vessel and two daughter vessels. Let the radius of the parent vessel be and the radius of each daughter vessel is and . The area ratio is defined as and the bifurcation index is . (a) Using the results from part (b) of problem 5.10, show that Solution The relationship between the flow rate in the parent vessel and the two daughter vessels is: This along with, We can relate flow rate and radius in this system, Solving for in terms of and : Substituting for is the definition of : (b) Determine the value of that leads to a minimum in the value of . What does this result imply about the area ratio? Solution Taking the first derivative of with respect to , Collecting terms and setting the derivative equal to zero, Simplifying The solution to the above equation is . The corresponding value of is...
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